Related papers: ROC curves for LDA classifiers

Pathologists routinely classify breast tumors according to recurring patterns of nuclear grades, cytoplasmic coloration, and large-scale morphological formations (i.e. streams of spindle cells, adenoid islands, etc.). The fact that there…

Receiver operating characteristic (ROC) analysis is a tool to evaluate the capacity of a numeric measure to distinguish between groups, often employed in the evaluation of diagnostic tests. Overall classification ability is sometimes…

In machine learning contests such as the ImageNet Large Scale Visual Recognition Challenge and the KDD Cup, contestants can submit candidate solutions and receive from an oracle (typically the organizers of the competition) the accuracy of…

In this paper we obtain an explicit formula for the number of curves in a compact complex surface $X$ (passing through the right number of generic points), that has up to one node and one singularity of codimension $k$, provided the total…

Let $W(z)$ be a $n\times n$ matrix polynomial with rational coefficients. Denote $C$ the spectral curve $\det \left( w\cdot{\bf 1}-W(z)\right) =0$. Under some natural assumptions about the structure of $W(z)$ we prove that certain…

For a certain class of varieties X, we derive a formula for the valuation d_{X} on the arc space L(Y) of a smooth ambient space Y, in terms of an embedded resolution of singularities. A simple transformation rule yields a formula for the…

For Classical compact Lie groups, we use Macdonald's formula \cite{Ma} and Ricci curvature for analyzing a "concentration locus", which is a tool to detect where a sequence of metric, Borel measurable spaces concentrates its measure.

To assess the classification accuracy of a continuous diagnostic result, the receiver operating characteristic (ROC) curve is commonly used in applications. The partial area under the ROC curve (pAUC) is one of widely accepted summary…

2D and 3D tumor features are widely used in a variety of medical image analysis tasks. However, for chemotherapy response prediction, the effectiveness between different kinds of 2D and 3D features are not comprehensively assessed,…

In clinical practice, multiple biomarkers are used for disease diagnosis, but their individual accuracies are often suboptimal, with only a few proving directly relevant. Effectively selecting and combining biomarkers can significantly…

Let J be the jacobian of a reduced projective curve C with nodes only. 1) We give a simple and natural definition for its many compactifications and show the connection with various other definitions appearing in the literature. 2) Among…

Functional markers become a more frequent tool in medical diagnosis. In this paper, we aim to define an index allowing to discriminate between populations when the observations are functional data belonging to a Hilbert space. We discuss…

Breast cancer is the most common malignant tumor among women and the second cause of cancer-related death. Early diagnosis in clinical practice is crucial for timely treatment and prognosis. Dynamic contrast-enhanced magnetic resonance…

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…

Recent work on privacy-preserving machine learning has considered how data-mining competitions such as Kaggle could potentially be "hacked", either intentionally or inadvertently, by using information from an oracle that reports a…

Here we develop some basic analytic tools to study compactness properties of $J$-curves (i.e. pseudo-holomorphic curves) when regarded as submanifolds. Incorporating techniques from the theory of minimal surfaces, we derive an inhomogeneous…

We define and count lattice points in the moduli space of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space. The enumeration produces polynomials with top…

This is the second in a series of three papers in which we investigate the rational Chow ring of the stack consisting of nodal curves of genus. Here we define the basic classes: the classes of strata and the Mumford classes.

Lame curves are a particular class of elliptic curves (with a torsion point attached to them) which naturally arise when studying Lame operators with finite monodromy. They can be realized as covers of the projective line unramified outside…

The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of…